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Chapter 1: Problem 2

Evaluate each expression for \(x=4\). $$x+10$$

Short Answer

Expert verified
The evaluated expression for \(x=4\) is 14.

Step by step solution

01

Identify the given values

In this case, the given expression is \(x + 10\) and the value of x is given as 4.
02

Substitute the given value of x

Substitute x=4 into the given expression. This would give us \(4 + 10\).
03

Evaluate the expression

Now, perform the addition operation which gives the result as 14.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Expression Evaluation
Expression evaluation involves calculating the value of a mathematical expression by assigning values to its variables. In the exercise, we're dealing with the expression \(x + 10\). This process starts by identifying the expression to be evaluated and noting any given values or constants.
Steps to Evaluate an Expression:
  • Identify the variables and constants in your expression. In our example, \(x\) is the variable and 10 is a constant.
  • Determine the value assigned to each variable, such as \(x = 4\), which is provided in the exercise.
  • Carry out the arithmetic operations required by the expression, which we'll cover in more detail later.
We'll delve deeper into how to substitute specific values next.
Substitution Method
The substitution method is a technique used to replace a variable in an expression with a given value. This is particularly useful in expressing real-world quantities with mathematical terms.Why Substitution Matters:
  • It removes the variable, turning the expression into a purely numerical problem.
  • Makes complex expressions simpler and easier to solve.
For our expression \(x + 10\), follow these steps:- Start with the original expression: \(x + 10\).- Substitute \(x\) with its given value, which is 4 in this case. You now have \(4 + 10\).By substituting, you allow for the next step, which is to evaluate using basic arithmetic operations.
Basic Arithmetic Operations
Basic arithmetic operations are fundamental math calculations including addition, subtraction, multiplication, and division. These are essential for solving substituted expressions.In our example, the expression becomes \(4 + 10\) after substitution.Here's how you perform these operations:
  • **Addition:** Add numbers together to get a sum. For \(4 + 10\), the sum is 14.
  • Although not needed for this specific case, it's useful to know other operations like subtraction, multiplication, and division can similarly solve expressions.
In summary, basic arithmetic enables you to finalize the value of an expression once variables have been replaced. Applying these core operations, we successfully evaluated our expression with the answer of 14.

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Most popular questions from this chapter

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The difference between \(-11\) and the quotient of 20 and \(-5\)

Without using a number line, describe how to add two numbers with different signs. Give an example.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { Simplify: } \frac{1}{4}-6(2+8) \div\left(-\frac{1}{3}\right)\left(-\frac{1}{9}\right)$$

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